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Direct measurements of the spin glass correlation function $G(R)$ forGaussian and bimodal Ising spin glasses in dimension two have been carried outin the temperature region $T \sim 1$. In the Gaussian case the data areconsistent with the known anomalous dimension value $\eta \equiv 0$. For thebimodal spin glass in this temperature region $T > T^{*}(L)$, well above thecrossover $T^{*}(L)$ to the ground state dominated regime, the effectiveexponent $\eta$ is clearly non-zero and the data are consistent with theestimate $\eta \sim 0.28(4)$ given by McMillan in 1983 from similarmeasurements. Measurements of the temperature dependence of the Binder cumulant$U_{4}(T,L)$ and the normalized correlation length $\xi(T,L)/L$ for the twomodels confirms the conclusion that the 2D bimodal model has a non-zeroeffective $\eta$ both below and above $T^{*}(L)$. The 2D bimodal and Gaussianinteraction distribution Ising spin glasses are not in the same Universalityclass.

The bimodal Ising spin glass in dimension two : the anomalous dimension $\eta$